"A rectangular swimming pool is to be built with an area of 1800 sq. feet. The owner wants 5-foot wide decks along either side, and 10-foot wide decks at both ends. Find the dimensions of the smallest piece of property on which the pool can be built satisfying these conditions."

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Nov 22nd 2006, 03:55 AM

earboth

Quote:

Originally Posted by Nitz456

"A rectangular swimming pool is to be built with an area of 1800 sq. feet. The owner wants 5-foot wide decks along either side, and 10-foot wide decks at both ends. Find the dimensions of the smallest piece of property on which the pool can be built satisfying these conditions."

Hello,

1. I've attached a sketch of the described swimming pool.

2. . Thus:

3. The area including the decks is:

. Now plug in the value of l:

4. . Expand the RHS of this equation:

5. This function has an extreme value (maximum or minimum, you are interested in the minimum) if the first derivative equals zero: